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Example 12.6

Example 12.6. A Financial Planning Model. Background Information. General Ford (GF) Auto Corporation is trying to determine what type of compact car to develop. Each model is assumed to generate sales for 10 years.

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Example 12.6

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  1. Example 12.6 A Financial Planning Model

  2. Background Information • General Ford (GF) Auto Corporation is trying to determine what type of compact car to develop. • Each model is assumed to generate sales for 10 years. • GF has gathered information about the following quantities through focus groups with the marketing and engineering departments.

  3. Background Information -- continued • Fixed cost of developing car. This cost is assumed to be normally distributed with a $2.3 billion mean and a standard deviation of $0.5 billion. • Variable production cost. This cost, which includes all variable production costs required to build a single car, is normally distributed for each model during year 1 with a mean and standard deviation of $7800 and $600. Each year after year 1 the variable production cost is the previous year’s multiplied by an inflation factor. Each year this inflation facto is assumed to be normally distributed with mean 1.05 and standard deviation 0.015. All production costs are assumed to occur at the ends of the respective years.

  4. Background Information -- continued • Selling price. The price in year 1 is already set at $11,800. After year 1 the price will increase by the same inflation factor that drives production costs. Like production costs, revenues from sales are assumed to occur at the ends of the respective years. • Demand. The demand for cars in year 1 is assumed to be normally distributed with a mean of 100,000. The standard deviation is 10,000. After year 1 the demand in the given year is assumed to be normally distributed with mean equal to the actual demand in the previous year and standard deviation 10,000. An implication of this assumption is that demands in successive years are not probabilistically independent.

  5. Background Information -- continued • Production. In any particular year GF plans to base its production policy on the probability distribution of demand for that year - before the actual demand for that year is observed. If demand in any given year is greater than production, then the excess demand is lost. If production in any year is greater than demand, GF will sell the excess cars at an end-of-year discount of 30%. • Interest rate. GF plans to use a 10% interest rate to discount future cash flows. • Given these assumptions, GF wants to develop a simulation model that will evaluate its NPV (net present value) for this new car over the 10-year time horizon.

  6. GFAUTO.XLS • The simulation model can be found in this file and appears on the next slide.

  7. Developing the Spreadsheet Model • The model can be formed as follows. • Inputs. Enter the various inputs in the shaded cell. • Production multiplier. The only real decision GF has to make is the multiplier k for its production level. To experiment with several values of this multiplier, enter the formula =RISKSIMTABLE({0.8, 1, 1.2}) in cell E20. Other (or more) values could be tried here. • Variable cost inflation factors. Rows 26-42 contain a single 10-year simulation. The approach is to enter appropriate formulas in column B and C for years 1 and 2, then copy the year 2 formulas to the columns for the other years, and finally calculate the values in rows 36, 39, 40 and 42. Begin by entering the variable production cost inflation factor relating year 2 to year 1 in cell C27 with the formula =RISKNORMAL(InflMean,InflStdev) and copying this to the rest of row 27.

  8. Developing the Spreadsheet Model -- continued • Production quantities. The production quantity in year 1 is based on the expected demand and the standard deviation of demand in year 1, so we enter the formula =Dem1Mean+ProdFactor*Dem1StDev in cell B28. For other years, the expected demand is the previous year’s actual demand, and this is used to calculate the production quantity. Therefore for year 2, enter the formula =B29+ProdFactor*Dem1StDev in cell B28 and copy it across to the rest of the row 28. • Demands. Generate a demand in year 1 in cell B29 with the formula =RISKNORMAL(Dem1Mean,Dem1Stdev). As in the previous step the expected demand for year 2 is the actual demand for year 1. So generate demand for year 2 in cell C29 with the formula=RISKNORMAL(29,DemStdev), and then copy it to the rest of row 29 to generate demands for the other years.

  9. Developing the Spreadsheet Model -- continued • Variable production costs. Generate the variable production cost for year 1 in cell B30 with the formula =RISKNORMAL(VC1Mean,VC1Stdev). Then use the inflation factor in row 27 to generate the variable production cost for year 2 in cell C30 with the formula =B30*C27 and copy this across to the rest of row 30. • Selling prices. Enter the (nonrandom) selling price for year 1 in cell B31 with the formula =Price1. Then generate the price for year 2 in cell C31 with the formula =B31*C27 and copy this across to the rest of row 31.

  10. Developing the Spreadsheet Model -- continued • Production costs. The production cost for any year is the production quantity multiplied by the variable production cost, so enter the formula =B28*B30 in cell B33 and copy it to the rest of row 33. • Revenues. The revenues in any year are calculated in one of two possible ways. If demand is greater than production quantity, then revenue is the sales price multiplied by the production quantity. If demand is less than the production quantity, then revenue is the sales price multiplied by the demand, plus the discounted sales price multiplied by the number of cars left over. Therefore, calculate the revenue for year 1 in cell B34 with the formula=IF(B28<B29,B31*B28,B31*(B29+(1-Discount)*(B28-B29)))and copy it to the rest of row 34.

  11. Developing the Spreadsheet Model -- continued • Fixed cost. Generate fixed cost of developing the car in cell B36 with the formula =RISKNORMAL(FCMean,FCStdev)*1000. • NPVs. Calculate the NPV of all production costs (in millions of dollars) in cell B39 with the formula =NPV(IntRate,Costs)Similarly, enter the formula =NPV(IntRate,Revenues) in cell B40 for revenues. • Total NPV. Finally calculate the total NPV in cell B42 with the formula =RISKOUTPUT( )+B40-B36-B39

  12. Using @Risk • Now that the spreadsheet is setup we can use the @Risk toolbar to run the simulation. • We set the number of iterations to 1000 and the number of simulations to 3. • After running @Risk, we obtain the summary measures for the total NPV shown on the next slide. • We see that the multiplier k definitely makes a difference.

  13. @Risk Results • Here is the summary results and simulations statistics.

  14. @Risk Results -- continued • Based on these results, GF might want to experiment with even larger values of k. • Higher values of k mean larger production quantities. • This will result in more end-of-year discounted sales, but it is evidently better than lost sales from insufficient supply. • The corresponding histogram for k = 1.2 appears on the next slide. It’s wide spread indicates the large amount of uncertainty about the 10-year NPV for this car.

  15. @Risk Results -- continued

  16. @Risk Results -- continued • GF could make a lot of money, or it could lose a lot. • We entered two representative values in the Left X and the Right X boxes. • They show that the probability of a negative NPV is slightly greater than 0.22 and the probability of NPV being less than $10 million is 0.65. • We certainly would not discourage the company from proceeding with this car, because there is a lot of potential for profit, but it should also be aware of the potential for loss.

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